eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2376-9556 2019-11-15 6 1 13 17 10.12691/ijpdea-6-1-2 IJPDEA2019612 article Fateh Allahabi fateh.allahabi@tu.edu.ye 1 Mohammad Abdulkawi Mahiub 2 Department of Mathematics, Faculty of Science, Thamar University, Yemen Department of Mathematics, Faculty of Science and Arts, Najran University, Saudi Arabia This work introduce a difference controls of players by using a new control method to completing a pursuit game. We study pursuit game problems for controlled partial differential equations of the parabolic type. We proved a theorem on pursuit game with mixed constraints, where pursuers control are subjected to integral (geometric) constraint and geometric (integral) constraint are imposed on evaders control. Moreover, we established the sufficient conditions for which pursuit is possible in the game considered. http://pubs.sciepub.com/ijpdea/6/1/2/ijpdea-6-1-2.pdf pursuit game admissibility control integral constraint geometric constraint